Meshfree Methods

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An Introduction to Meshfree Methods and Their Programming

G.R. Liu,Y.T. Gu
An Introduction to Meshfree Methods and Their Programming Book PDF

Author : G.R. Liu,Y.T. Gu
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 52,5 Mb
Release : 2005-12-05
Category : Technology & Engineering
ISBN : 9781402034688

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An Introduction to Meshfree Methods and Their Programming by G.R. Liu,Y.T. Gu Pdf

The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

Mesh Free Methods

G.R. Liu
Mesh Free Methods Book PDF

Author : G.R. Liu
Publisher : CRC Press
Page : 715 pages
File Size : 48,6 Mb
Release : 2002-07-29
Category : Mathematics
ISBN : 9781420040586

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Mesh Free Methods by G.R. Liu Pdf

As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now,

Extended Finite Element and Meshfree Methods

Timon Rabczuk,Jeong-Hoon Song,Xiaoying Zhuang,Cosmin Anitescu
Extended Finite Element and Meshfree Methods Book PDF

Author : Timon Rabczuk,Jeong-Hoon Song,Xiaoying Zhuang,Cosmin Anitescu
Publisher : Academic Press
Page : 638 pages
File Size : 47,7 Mb
Release : 2019-11-13
Category : Technology & Engineering
ISBN : 9780128141076

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Extended Finite Element and Meshfree Methods by Timon Rabczuk,Jeong-Hoon Song,Xiaoying Zhuang,Cosmin Anitescu Pdf

Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications. Explains all the important theory behind XFEM and meshfree methods Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods Introduces alternative modeling methods to help readers decide what is most appropriate for their work

Meshfree Methods

G.R. Liu
Meshfree Methods Book PDF

Author : G.R. Liu
Publisher : CRC Press
Page : 772 pages
File Size : 41,8 Mb
Release : 2009-10-06
Category : Mathematics
ISBN : 9781420082104

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Meshfree Methods by G.R. Liu Pdf

Understand How to Use and Develop Meshfree TechniquesAn Update of a Groundbreaking WorkReflecting the significant advances made in the field since the publication of its predecessor, Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition systematically covers the most widely used meshfree methods. With 70% new material, this edit

Meshfree Particle Methods

Shaofan Li,Wing Kam Liu
Meshfree Particle Methods Book PDF

Author : Shaofan Li,Wing Kam Liu
Publisher : Springer Science & Business Media
Page : 509 pages
File Size : 48,5 Mb
Release : 2007-03-07
Category : Mathematics
ISBN : 9783540222569

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Meshfree Particle Methods by Shaofan Li,Wing Kam Liu Pdf

Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods, and multiscale methods. Most theories, computational formulations, and simulation results presented are recent developments in meshfree methods. They were either just published recently or even have not been published yet, many of them resulting from the authors ́ own research. The presentation of the technical content is heuristic and explanatory with a balance between mathematical rigor and engineering practice. It can be used as a graduate textbook or a comprehensive source for researchers, providing the state of the art on Meshfree Particle Methods.

Meshfree Methods for Partial Differential Equations II

Michael Griebel,Marc Alexander Schweitzer
Meshfree Methods for Partial Differential Equations II Book PDF

Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 40,8 Mb
Release : 2006-09-21
Category : Mathematics
ISBN : 9783540270997

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Meshfree Methods for Partial Differential Equations II by Michael Griebel,Marc Alexander Schweitzer Pdf

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Second International Workshop on Meshfree Methods held in September 2003 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this new and exciting area of interdisciplinary research and to present recent advances and results in this field.

Meshfree Methods for Partial Differential Equations

Michael Griebel,Marc A. Schweitzer
Meshfree Methods for Partial Differential Equations Book PDF

Author : Michael Griebel,Marc A. Schweitzer
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642561030

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Meshfree Methods for Partial Differential Equations by Michael Griebel,Marc A. Schweitzer Pdf

Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

Meshless Methods and Their Numerical Properties

Hua Li,Shantanu S. Mulay
Meshless Methods and Their Numerical Properties Book PDF

Author : Hua Li,Shantanu S. Mulay
Publisher : CRC Press
Page : 429 pages
File Size : 46,5 Mb
Release : 2013-02-22
Category : Mathematics
ISBN : 9781466517479

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Meshless Methods and Their Numerical Properties by Hua Li,Shantanu S. Mulay Pdf

Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the m

Meshfree Approximation Methods with MATLAB

Gregory E. Fasshauer
Meshfree Approximation Methods with MATLAB Book PDF

Author : Gregory E. Fasshauer
Publisher : World Scientific
Page : 520 pages
File Size : 40,5 Mb
Release : 2007
Category : Technology & Engineering
ISBN : 9789812706331

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Meshfree Approximation Methods with MATLAB by Gregory E. Fasshauer Pdf

Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.

Meshless Methods in Solid Mechanics

Youping Chen,James Lee,Azim Eskandarian
Meshless Methods in Solid Mechanics Book PDF

Author : Youping Chen,James Lee,Azim Eskandarian
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 41,5 Mb
Release : 2006-12-31
Category : Science
ISBN : 9780387333687

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Meshless Methods in Solid Mechanics by Youping Chen,James Lee,Azim Eskandarian Pdf

This book covers the fundamentals of continuum mechanics, the integral formulation methods of continuum problems, the basic concepts of finite element methods, and the methodologies, formulations, procedures, and applications of various meshless methods. It also provides general and detailed procedures of meshless analysis on elastostatics, elastodynamics, non-local continuum mechanics and plasticity with a large number of numerical examples. Some basic and important mathematical methods are included in the Appendixes. For readers who want to gain knowledge through hands-on experience, the meshless programs for elastostatics and elastodynamics are provided on an included disc.

Simulation of Additive Manufacturing using Meshfree Methods

Christian Weißenfels
Simulation of Additive Manufacturing using Meshfree Methods Book PDF

Author : Christian Weißenfels
Publisher : Springer Nature
Page : 207 pages
File Size : 46,7 Mb
Release : 2021-10-29
Category : Technology & Engineering
ISBN : 9783030873370

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Simulation of Additive Manufacturing using Meshfree Methods by Christian Weißenfels Pdf

This book provides a detailed instruction to virtually reproduce the processes of Additive Manufacturing on a computer. First, all mathematical equations needed to model these processes are presented. Due to their flexibility, meshfree methods represent optimal computational solution schemes to simulate Additive Manufacturing processes. On the other hand, these methods usually do not guarantee an accurate solution. For this reason, this monograph is dedicated in detail to the necessary criteria for computational solution schemes to provide accurate results. Several meshfree methods are examined with respect to these conditions. Two different 3D printing techniques are presented in detail. The results obtained from the simulation are investigated and compared with experimental data. This work is addressed to both scientists and professionals working in the field of development who are interested to learn the secrets behind meshfree methods or get into the modeling of Additive Manufacturing.

Meshfree Methods for Partial Differential Equations IX

Michael Griebel,Marc Alexander Schweitzer
Meshfree Methods for Partial Differential Equations IX Book PDF

Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer
Page : 206 pages
File Size : 45,6 Mb
Release : 2019-06-19
Category : Mathematics
ISBN : 9783030151195

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Meshfree Methods for Partial Differential Equations IX by Michael Griebel,Marc Alexander Schweitzer Pdf

This volume collects selected papers presented at the Ninth International Workshop on Meshfree Methods held in Bonn, Germany in September 2017. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. While the fundamental theory of meshfree methods has been developed and considerable advances of the various methods have been made, many challenges in the mathematical analysis and practical implementation of meshfree methods remain. This symposium aims to promote collaboration among engineers, mathematicians, and computer scientists and industrial researchers to address the development, mathematical analysis, and application of meshfree and particle methods especially to multiscale phenomena. It continues the 2-year-cycled Workshops on Meshfree Methods for Partial Differential Equations.

Meshfree Methods for Partial Differential Equations V

Michael Griebel,Marc Alexander Schweitzer
Meshfree Methods for Partial Differential Equations V Book PDF

Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 47,7 Mb
Release : 2010-11-04
Category : Mathematics
ISBN : 9783642162299

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Meshfree Methods for Partial Differential Equations V by Michael Griebel,Marc Alexander Schweitzer Pdf

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.

Meshfree Methods for Partial Differential Equations VI

Michael Griebel,Marc Alexander Schweitzer
Meshfree Methods for Partial Differential Equations VI Book PDF

Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 54,5 Mb
Release : 2012-12-16
Category : Computers
ISBN : 9783642329791

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Meshfree Methods for Partial Differential Equations VI by Michael Griebel,Marc Alexander Schweitzer Pdf

Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers presented at the Sixth International Workshop on Meshfree Methods held in Bonn, Germany in October 2011. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. ​

Meshfree Methods for Partial Differential Equations VII

Michael Griebel,Marc Alexander Schweitzer
Meshfree Methods for Partial Differential Equations VII Book PDF

Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer
Page : 323 pages
File Size : 49,5 Mb
Release : 2014-12-02
Category : Mathematics
ISBN : 9783319068985

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Meshfree Methods for Partial Differential Equations VII by Michael Griebel,Marc Alexander Schweitzer Pdf

Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.